Question

If m is mass of electron, v its velocity, r is the radius of stationary circular orbit around a nucleus
with charge Ze, them from Bohr's first postulate, the speed v of the electron in CGS system in the
orbit is proportional to :

1) (mr / Ze^2)^-1/2

2) mr / Ze^2

3) Ze^2 / mr

4) (Ze^2 / mr)^-1/2​

Answer 1

Answer:

Answer :

A

Solution :

In the revolution of electron, coulomb force provides the necessary centripetal force <br>

4_S01.png" width="80%">

Answer 2

Answer:

The correct option is (1). If m is the mass of the electron, v its velocity, and r is the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's first postulate, the speed v of the electron in the CGS system in the orbit is proportional to (mr / Ze²)^-1/2

Explanation:

• In the Bohr atomic model, electrons circle the nucleus in well-defined circular orbits. The quantum number n, an integer, is used to identify the orbits. By releasing or absorbing energy, electrons can change orbits.
• In contrast to what electromagnetic theory predicted, Bohr's first postulate stated that an atom's electron might rotate in some stable orbits without emitting radiant energy. This postulate holds that every atom has a set of distinct stable states in which it can reside and that each such state has distinct total energy. These are referred to as the atom's stationary states.
• Centripetal force = electrostatic force of attraction
• mv²/r = 1/4πε₀ × Ze²/r²
• Therefore, v² = Ze²/ 4πε₀mr
• It can also be expressed as, v = (mr / Ze²)^-1/2

Thus, If m is the mass of the electron, v its velocity, and r is the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's first postulate, the speed v of the electron in the CGS system in the orbit is proportional to (mr / Ze²)^-1/2

#SPJ3